Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design

In this paper, the adaptive backstepping design is proposed for the full state hybrid projective synchronization between two different chaotic systems with fully unknown parameters. Based on the design, the synchronization of two uncertain chaotic systems is realized only by using one controller, and the unknown parameters are identified through the corresponding parameter update laws. The uncertain Genesio–Tesi chaotic system and Lorenz system are chosen as examples for detailed description of the method. Finally, some numerical simulations are given to illustrate the effectiveness of the proposed method.